In surfing, the rider is going down the line (not down the fall line) and is either frontside or backside. While going frontside or backside the surfer will make turns that are essentially what a snowboarder might call toeside and heelside. Surfers call them top turns and bottom turns and since the turns are happening at the top and bottom of the wave, those terms work well for surfing.
Frontside/backside are not descriptions of a specific turn on a wave, they are descriptions of which way a surfer is going on a wave related to which foot they have forward.
Typically a snowboarder is going down the fall line. It is not the same orientation as going down the line in surfing. It doesn't make sense to use the terms frontside turn or backside turn because alternating turns would be frontside/backside/frontside/backside....down the fall line. The snowboarder turns going down the slope are the surfing equivalent of top turn/bottom turn, not frontside/backside. But top turn/bottom turn makes no sense when going down the fall line on a snowboard. That is why snowboarders use the terms heelside turn/toeside turn. Those terms make sense for snowboarding and that is probably why, even though plenty of surfers also snowboard, heelside/toeside are pretty much universally (at least everywhere I have been in the US) used for snowboarding.
Now if a snowboarder finds a nice bank that is frontside or backside and the snowboarder gets to make top turns and bottom turns, the surfing terms make sense and are often used along with hoots of joy!
In my avatar, if I was surfing, that turn could be the beginning of a frontside bottom turn or the end of a backside top turn. It is not necessarily a frontside turn. In snowboarding it is simply a toeside turn.